Editing Thermodynamic temperature (section)

=== Diffusion of thermal energy: black-body radiation ===
<!-- NOTE TO EDITORS: This section is internally linked from elsewhere within the article. -->

[[Image:Wiens law.svg|thumb|upright=1.4|'''Figure 5''' The spectrum of black-body radiation has the form of a Planck curve. A 5500&nbsp;K black-body has a peak emittance wavelength of 527&nbsp;nm. Compare the shape of this curve to that of a Maxwell distribution in ''[[#Nature of kinetic energy, translational motion, and temperature|Fig.&nbsp;2]]''&nbsp;above.]]
[[Thermal radiation]] is a byproduct of the collisions arising from various vibrational motions of atoms. These collisions cause the electrons of the atoms to emit thermal [[photon]]s (known as [[black-body radiation]]). Photons are emitted anytime an electric charge is accelerated (as happens when electron clouds of two atoms collide). Even ''individual molecules'' with internal temperatures greater than absolute zero also emit black-body radiation from their atoms. In any bulk quantity of a substance at equilibrium, black-body photons are emitted across a range of [[wavelength]]s in a spectrum that has a bell curve-like shape called a [[Planck's law of black body radiation|Planck curve]] (see graph in ''Fig.&nbsp;5'' at right). The top of a Planck curve ([[Wien's displacement law|the peak emittance wavelength]]) is located in a particular part of the [[electromagnetic spectrum]] depending on the temperature of the black-body. Substances at extreme [[cryogenics|cryogenic]] temperatures emit at long radio wavelengths whereas extremely hot temperatures produce short [[gamma ray]]s (see {{section link|#Table of thermodynamic temperatures}}).

Black-body radiation diffuses thermal energy throughout a substance as the photons are absorbed by neighboring atoms, transferring momentum in the process. Black-body photons also easily escape from a substance and can be absorbed by the ambient environment; kinetic energy is lost in the process.

As established by the [[Stefan–Boltzmann law]], the intensity of black-body radiation increases as the fourth power of absolute temperature. Thus, a black-body at 824&nbsp;K (just short of glowing dull red) emits 60 times the radiant [[Power (physics)|power]] as it does at 296&nbsp;K (room temperature). This is why one can so easily feel the radiant heat from hot objects at a distance. At higher temperatures, such as those found in an [[Incandescent light bulb|incandescent lamp]], black-body radiation can be the principal mechanism by which thermal energy escapes a system.

==== Table of thermodynamic temperatures ====
The table below shows various points on the thermodynamic scale, in order of increasing temperature.

{| class="wikitable" style="text-align:center"
|-
!
!Kelvin
!Peak emittance<br />[[wavelength]]<ref>The cited emission wavelengths are for true black bodies in equilibrium. In this table, only the sun so qualifies. [https://physics.nist.gov/cgi-bin/cuu/Value?bwien CODATA recommended value] of {{val|2.897771955|end=...|e=-3|u=m⋅K}} used for Wien displacement law constant ''b''.</ref> of<br />[[Wien's displacement law|black-body photons]]
|-
|style="text-align:right"|[[Absolute zero]]<br />(precisely by definition)
|0 K
|{{resize|140%|[[Infinity|∞]]}}<ref name="T0"/>
|-
|style="text-align:right"|Coldest measured<br />temperature<ref name="recordcold">A record cold temperature of 450&nbsp;±80&nbsp;pK in a Bose–Einstein condensate (BEC) of sodium (<sup>23</sup>Na) atoms was achieved in 2003 by researchers at [[Massachusetts Institute of Technology|MIT]]. {{cite journal |title=Cooling Bose–Einstein Condensates Below 500 Picokelvin |first=A. E. |last=Leanhardt |display-authors=etal |journal=Science |volume=301 |issue=5639 |date=12 September 2003 |page=1515|doi=10.1126/science.1088827 |pmid=12970559 |bibcode=2003Sci...301.1513L }} The thermal velocity of the atoms averaged about 0.4&nbsp;mm/s. This record's peak emittance black-body radiation wavelength of 6,400 kilometers is roughly the radius of Earth.</ref>
|450 [[Orders of magnitude (temperature)#SI multiples|pK]]
|6,400 [[Kilometre|km]]
|-
|style="text-align:right"|One [[Orders of magnitude (temperature)#SI multiples|millikelvin]]<br />(precisely by definition)
|0.001 K
|2.897&nbsp;77 [[Metre|m]]<br /> (radio, [[FM broadcasting|FM band]])<ref>The peak emittance wavelength of 2.897&nbsp;77&nbsp;m is a frequency of 103.456&nbsp;MHz.</ref>
|-
|style="text-align:right"|[[Cosmic microwave background|cosmic microwave<br />background radiation]]
|2.725&nbsp;K
|1.063&nbsp;[[Metre|mm]] (peak wavelength)
|-
|style="text-align:right"|[[Vienna Standard Mean Ocean Water|Water]]'s [[triple point]]
|273.16 K
|10.6083 [[Metre#SI prefixed forms of metre|μm]]<br />(long wavelength [[Infrared|I.R.]])
|-
|style="text-align:right"|[[ISO 1]] standard temperature<br />for precision [[metrology]]<br />(precisely 20&nbsp;°C by definition)
|293.15 K
|{{val|9.88495}}&nbsp;μm<br />(long wavelength [[Infrared|I.R.]])
|-
|-
|style="text-align:right"|[[Incandescent light bulb|Incandescent lamp]]{{efn-ua|For a true black body (which tungsten filaments are not). Tungsten filaments' emissivity is greater at shorter wavelengths, which makes them appear whiter.}}
|2500 K{{efn-ua|The 2500&nbsp;K value is approximate.}}
|1.16&nbsp;μm<br />(near [[infrared]]){{efn-ua|name=Photosphere|Effective photosphere temperature.}}<!--Should this be here?-->
|-
|[[Sun]]'s visible surface<ref>{{Cite web |year=2015 |title=Resolution B3 on recommended nominal conversion constants for selected solar and planetary properties |url=https://iau.org/static/resolutions/IAU2015_English.pdf}}</ref><ref>{{Cite book |last1=Hertel |first1=Ingolf V. |url=https://books.google.com/books?id=vr0UBQAAQBAJ&dq=5772+K+sun&pg=PA35 |title=Atoms, Molecules and Optical Physics 1: Atoms and Spectroscopy |last2=Schulz |first2=Claus-Peter |date=2014-10-24 |publisher=Springer |isbn=978-3-642-54322-7 |pages=35 |language=en}}</ref><ref>{{Cite book |last1=Vignola |first1=Frank |url=https://books.google.com/books?id=q9WlDwAAQBAJ&dq=5772+K+sun&pg=PP26 |title=Solar and Infrared Radiation Measurements |edition=2nd |last2=Michalsky |first2=Joseph |last3=Stoffel |first3=Thomas |date=2019-07-30 |publisher=CRC Press |isbn=978-1-351-60020-0 |pages=chapter 2.1, 2.2 |language=en}}</ref><ref>{{Cite web |title=Sun Fact Sheet |url=https://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html |access-date=2023-08-27 |website=NASA Space Science Center Coordinated Archive}}</ref>
|5772 K
|502&nbsp;[[Metre#SI prefixed forms of metre|nm]]<br />([[Color#Spectral colors|green light]])
|-
|style="text-align:right"|[[Lightning|Lightning bolt's]]<br />channel
|28,000 K
|100&nbsp;nm<br />(far [[ultraviolet]] light)
|-
|style="text-align:right"|[[Sun#Core|Sun's core]]
|16 [[Orders of magnitude (temperature)#SI multiples|MK]]
|0.18&nbsp;nm ([[X-ray]]s)
|-
|style="text-align:right"|[[Thermonuclear explosion]]<br />(peak temperature)<ref>The 350&nbsp;MK value is the maximum peak fusion fuel temperature in a thermonuclear weapon of the Teller–Ulam configuration (commonly known as a "hydrogen bomb"). Peak temperatures in Gadget-style fission bomb cores (commonly known as an "atomic bomb") are in the range of 50 to 100&nbsp;MK. {{cite web |title=Nuclear Weapons Frequently Asked Questions |at=3.2.5 Matter At High Temperatures |url=http://nuclearweaponarchive.org/Nwfaq/Nfaq3.html#nfaq3.2}}{{fcn|{{subst:DATE}}|date=September 2024}} All referenced data was compiled from publicly available sources.</ref>
|align="center"|350 MK
|align="center"|8.3 × 10<sup>−3</sup> nm<br />([[gamma ray]]s)
|-
|style="text-align:right"|Sandia National Labs'<br />[[Z Pulsed Power Facility|Z machine]]{{efn-ua|For a true black body (which the plasma was not). The Z machine's dominant emission originated from 40&nbsp;MK electrons (soft x–ray emissions) within the plasma.}}<ref>Peak temperature for a bulk quantity of matter was achieved by a pulsed-power machine used in fusion physics experiments. The term "bulk quantity" draws a distinction from collisions in particle accelerators wherein high "temperature" applies only to the debris from two subatomic particles or nuclei at any given instant. The >2&nbsp;GK temperature was achieved over a period of about ten nanoseconds during "shot Z1137". In fact, the iron and manganese ions in the plasma averaged 3.58 ±0.41&nbsp;GK (309 ±35&nbsp;keV) for 3&nbsp;ns (ns 112 through 115). {{cite journal |title=Ion Viscous Heating in a Magnetohydrodynamically Unstable Z Pinch at Over 2&nbsp;×&nbsp;10<sup>9</sup> Kelvin |first=M. G. |last=Haines |display-authors=etal |journal=Physical Review Letters |volume=96 |issue=7 |id=No. 075003 |year=2006 |page=075003 |doi=10.1103/PhysRevLett.96.075003|pmid=16606100 |bibcode=2006PhRvL..96g5003H }} For a press summary of this article, see {{cite web |date=March 8, 2006 |title=Sandia's Z machine exceeds two billion degrees Kelvin |publisher=Sandia |url=http://www.sandia.gov/news-center/news-releases/2006/physics-astron/hottest-z-output.html |archive-url=https://web.archive.org/web/20060702185740/http://www.sandia.gov/news-center/news-releases/2006/physics-astron/hottest-z-output.html |archive-date=2006-07-02 }}</ref>
|2 [[Orders of magnitude (temperature)#SI multiples|GK]]
|1.4 × 10<sup>−3</sup> nm<br />(gamma rays)
|-
|style="text-align:right"|Core of a [[Silicon-burning process|high-mass star on its last day]]<ref>Core temperature of a high–mass (>8–11 solar masses) star after it leaves the main sequence on the [[Hertzsprung–Russell diagram]] and begins the [[Alpha reactions|alpha process]] (which lasts one day) of [[Silicon burning process|fusing silicon–28]] into heavier elements in the following steps: sulfur–32 → argon–36 → calcium–40 → titanium–44 → chromium–48 → iron–52 → nickel–56. Within minutes of finishing the sequence, the star explodes as a Type&nbsp;II [[supernova]].</ref>
|align="center"|3 GK
|align="center"|1 × 10<sup>−3</sup> nm<br />(gamma rays)
|-
|style="text-align:right"|Merging binary [[neutron star]] system<ref>Based on a computer model that predicted a peak internal temperature of 30 MeV (350&nbsp;GK) during the merger of a binary neutron star system (which produces a gamma–ray burst). The neutron stars in the model were 1.2 and 1.6 solar masses respectively, were roughly 20&nbsp;km in diameter, and were orbiting around their barycenter (common center of mass) at about 390&nbsp;Hz during the last several milliseconds before they completely merged. The 350&nbsp;GK portion was a small volume located at the pair's developing common core and varied from roughly 1 to 7&nbsp;km across over a time span of around 5&nbsp;ms. Imagine two city-sized objects of unimaginable density orbiting each other at the same frequency as the G4 musical note (the 28th white key on a piano). At 350&nbsp;GK, the average neutron has a vibrational speed of 30% the speed of light and a relativistic mass 5% greater than its rest mass. {{cite journal|arxiv=astro-ph/0507099v2|doi=10.1111/j.1365-2966.2006.10238.x|title=Torus formation in neutron star mergers and well-localized short gamma-ray bursts|journal=Monthly Notices of the Royal Astronomical Society|volume=368|issue=4|pages=1489–1499|year=2006|last1=Oechslin|first1=R.|last2=Janka|first2=H.-T.|doi-access=free |bibcode=2006MNRAS.368.1489O|s2cid=15036056}} For a summary, see {{cite web|url=http://www.mpa-garching.mpg.de/mpa/research/current_research/hl2005-10/hl2005-10-en.html |title=Short Gamma-Ray Bursts: Death Throes of Merging Neutron Stars |publisher=Max-Planck-Institut für Astrophysik |access-date=24 September 2024}}</ref>
|350 GK
|8 × 10<sup>−6</sup> nm<br />(gamma rays)
|-
|style="text-align:right"|[[Gamma-ray burst progenitors]]<ref>{{cite magazine |magazine=New Scientist |url=https://www.newscientist.com/article/mg20928026.300-eight-extremes-the-hottest-thing-in-the-universe.html |title=Eight extremes: The hottest thing in the universe |first=Stephen |last=Battersby |date=2 March 2011 |quote=While the details of this process are currently unknown, it must involve a fireball of relativistic particles heated to something in the region of a trillion kelvin.}}</ref>
|1 [[Orders of magnitude (temperature)#SI multiples|TK]]
|3 × 10<sup>−6</sup> nm<br />(gamma rays)
|-
|style="text-align:right"|[[CERN]]'s proton vs. nucleus collisions<ref>{{cite web |url=http://public.web.cern.ch/public/Content/Chapters/AboutCERN/HowStudyPrtcles/HowSeePrtcles/HowSeePrtcles-en.html |url-status=dead |title=How do physicists study particles? |archive-url=https://web.archive.org/web/20071011103924/http://public.web.cern.ch/Public/Content/Chapters/AboutCERN/HowStudyPrtcles/HowSeePrtcles/HowSeePrtcles-en.html |archive-date=2007-10-11 |publisher=CERN}}</ref>
|10 TK
|3 × 10<sup>−7</sup> nm<br />(gamma rays)
|-
|}
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